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Expressions using Letter-Numbers - Simplification of Algebraic Expressions

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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An algebraic expression is formed from variables (letter-numbers) and constants using operations like addition, subtraction, multiplication, and division.

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Terms are the parts of an expression that are added. For example, in 4x2−3xy4x^2 - 3xy, the terms are 4x24x^2 and −3xy-3xy.

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A factor is a part of a term. In the term 5xy5xy, the factors are 55, xx, and yy.

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The numerical factor of a term is called its numerical coefficient. In −7ab-7ab, the coefficient is −7-7.

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Like Terms are terms which have the same algebraic (literal) factors. For example, 2xy2xy and −5xy-5xy are like terms because both have xyxy as literal factors.

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Unlike Terms are terms which have different algebraic factors. For example, 3x23x^2 and 3x3x are unlike terms.

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Simplification of an algebraic expression is the process of combining like terms by adding or subtracting their numerical coefficients.

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An expression with one term is a Monomial, two terms is a Binomial, and three terms is a Trinomial. Any expression with one or more terms is a Polynomial.

📐Formulae

ax+bx=(a+b)xax + bx = (a + b)x

ax−bx=(a−b)xax - bx = (a - b)x

−(a+b)=−a−b-(a + b) = -a - b

−(a−b)=−a+b-(a - b) = -a + b

💡Examples

Problem 1:

Simplify the expression: 21b−32+7b−20b21b - 32 + 7b - 20b

Solution:

21b+7b−20b−3221b + 7b - 20b - 32 (21+7−20)b−32(21 + 7 - 20)b - 32 8b−328b - 32

Explanation:

To simplify, we group the like terms (terms containing bb) together and then combine their numerical coefficients. The constant term −32-32 remains as it is.

Problem 2:

Subtract a−ba - b from 3a−b+43a - b + 4.

Solution:

(3a−b+4)−(a−b)(3a - b + 4) - (a - b) =3a−b+4−a+b= 3a - b + 4 - a + b =3a−a−b+b+4= 3a - a - b + b + 4 =2a+0+4= 2a + 0 + 4 =2a+4= 2a + 4

Explanation:

When subtracting, we change the sign of every term in the expression being subtracted. Then, we group the like terms 3a,−a3a, -a and −b,b-b, b and simplify.

Problem 3:

Find the value of the expression x2+2x+1x^2 + 2x + 1 when x=−2x = -2.

Solution:

Substitute x=−2x = -2 into the expression: (−2)2+2(−2)+1(-2)^2 + 2(-2) + 1 =4−4+1= 4 - 4 + 1 =1= 1

Explanation:

To find the value of an algebraic expression, we replace the variable with the given numerical value and perform the arithmetic operations.

Problem 4:

Simplify by combining like terms: (3y2+5y−4)−(8y−y2−4)(3y^2 + 5y - 4) - (8y - y^2 - 4)

Solution:

3y2+5y−4−8y+y2+43y^2 + 5y - 4 - 8y + y^2 + 4 =(3y2+y2)+(5y−8y)+(−4+4)= (3y^2 + y^2) + (5y - 8y) + (-4 + 4) =4y2−3y+0= 4y^2 - 3y + 0 =4y2−3y= 4y^2 - 3y

Explanation:

First, remove the parentheses. Note that the minus sign outside the second bracket changes the signs of all terms inside. Then, group like terms (y2y^2 terms, yy terms, and constants) and combine them.